Angular displacement is usually2nsjqo2 edq0br5mz 1 s zj r,y363pyh9 express in units of

  Angular velocity is exdz u3 nm+cprh ,j* ext-s61nb,pressed in units of

  Angular acceleration is expressed in units );(/a3cxqtiw9v wdh mof

  A boy and a girl are riding on a merry-go-round which is turning at a constant rqqw 3 f0qe5f/vhh/8zx7l6: svtf4l vr( kvzt9ate. The boy is nea tv3qll/fvft4z8(hkrez0v qqv6/7w: s fhx 95r the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turningw7j tq5i9e *hm at a constant rate. The boy is near the outer 9 jw57iethq m*edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding ozaw;2r *i59lkrnvw : 2sulbd9 n a merry-go-round which is turning at a constant r2 d9vs rl;arzu 9w :i2wbln5*kate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turnin0 k ;a 2c e;:zotcricnk;-s9mkg at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accelera:2o9-sm ;kirc;n;tkkc z 0eac tion?

  A boy and a girl are riding a merry--k(t b;b7 ym5ekvqr rnv(+n2 ngo-round which is turning at a constant rate. The boy is near the outer edge, while the (qr2ten-;rnbyv7+n k(km 5vb girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whmo3k))pkf.semq5ib:z4o 5er+fyb * oich of the following is an accurate state)fz *boerk)oe.q: bmy4psof +355 im kment?

  Rolling without slipping depends ovs33, cvmwyahg)f+ gjhck3u o0e9e -/n

  Two equal forces are applied to a door. The fi0z)wxrke19 m nrst force is applied at the midpoint of the door; thek9e nmx r01)wz second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. kr9av+ 7u gf6(ab(o 6md gv6yhThe first force is applied perpendicular to the door; the secon 66agovr96m+7 ayhdv(u( bkfg d force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to h)9yqdl -6dwhu t;dq ,a doorknob, perpendicular to the door. The first force is twice as large as the seconwhqdu; 9dhq )-ydl, 6td force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measu s6jibxr7 i.sn/.dp3 hre an object's resistance to changes in rotation?36p n.rsb. id hs7xi/j

  Consider two uniform solid spheres whehp le7mbhl,p r527v4mre both have the same diameter, but one has twice the mass of the other. The rap7 hmv7emhr 5lb2,4l ptio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, buz+bfgmtdv( 9 8t one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smadzgmvtb+98(f ller sphere is

  Consider two uniform solid spheres where one has twice the mass w3tt;wka nr; ugf5;u: /er0jm and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia iswa;um w u0t/et;j5r; :f 3ngkr

  A uniform solid sphere has mass M and radi0eo*bll/.f ai 2w wj)h,,qft0f qxkc*eqah-4 us R. If these are increased to 2M and 3R, what ha4flq hajwbtik)q *lefh./ ex o- 0c*,w20q,fa ppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that qpeb/s 4ft6t,e, o:j pobject will

  The moment of inertia of a s/t vn:nen *w4ycv.q+zolid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy i / vw4+ynqc:zvnen *t.s

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of+bbxo( , ov1ol7t+fi k 10 kg and a radius of 30 cm. What is fli+o+,b(o7 vk xto1bthe ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and r .od 8c7vk:ty/ n pd/xwr(aox2adius R rolls without slipping down an inclined plane starting from rest. The lineart 2x .d /:(pn 8rdxoko/7vawcy velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witho7z v4bv7.svs t1w(fubut slipping down an inclined plane starting from rest. The angular velocity of the sphe7b4vf17v .bsswv(zu t re at the bottom of the incline depends on

  "The total angular momentum of a system of particles changefy*w3 :-ykpgk fa4dj3s when a net external force acts on the system." 4ayj*ky 3fgp 3dwf:-kThis statement is

  In what circumstances can the angular velocity of system of partzx-9hqdezr* u3 sr/5uicles change without any chang3xqzr/59hz uds-ue*re in the system's angular momentum?

  The Earth orbits the Sun in an ellipticrs l 92lk9pab:al orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about t l9sr abpk:92lhe Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves clox yvcn( eru8.0/b-z8*w p q5p ,exretvse to the Sun, then which of the following best describes the orbiting speed of the tur v8zve r* 5cx x p/.pwq,y-ene8(b0Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched 6t6w*jevyo n w3 r* bnmy9,p8tarms closeowe** w yp rb6n6t tn93jm8,yv to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouet ,8 :4r;ymx3vmggt ybdte (a fast spin) by pulling in his outstretched a4:br y mgg3md; xvt,y8rms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs ysml0jqyx-/ tr73.aihzywaf :. t5;xa pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia ab jta7yr50lywz.fy s-hxt :ix/ qm.a;3out the axis of rotation?

State the law of conservation of angula8asvt s5bx h1 mcosnqt.5*+y9 r momentum.

  What arc length does the Earth travel in a three month)iuyrk d,dn 13 period in its nearly circular orbk1 unird) 3y,dit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a 1(*ckjmzusnb) : ,a rxmyi7w;clock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 seconds;(m1kcs7xi j) rawbn:,m zu*y?

  How many rad/s is 25 revolutionssz xov-t .lb)tl8s1h/ per minute equivalent to?

  A bicycle wheel rotates unifo 9k 6jua ate7m 3)gxwd.r q,dc:wmj,s9rmly through 2.0 revolutions in 4.0 s. What is the frequency of the whee3cj)9wed ,9 7uma.x mkjdgq ra:s, 6wtl's rotation?

  A pulsar (a rotating neutron star;dw bm ,b ;r5ct)wfslpwsawp(0+ /qv o088 ece) emits pulses at a frequency of 0.40 kHz. The period of its rotation i+ wtdec0p wmp(oss,vw8q0c)brl/; 58e;b afws

  A phonograph record rotates at 45 rpm. Through whge5 x .wfo,h8.b;jhw/b/ms lxat angle does it turn in 0.20 w/el ./ fsow;gm8h xb5bjhx,.s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poin*qjj9 bpo* g;o6b,t39z mglnr t on the outer rim move inb r;*, p lzg6tj*o 9mojgbn3q9 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions kw7mjeu1 7-7/i9 ezsb( yikjwin 4.0 s. What is the average an9wew7be 7 jy/(-s7iuj mik1k zgular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revo( cczp6o b,ho2lutions in 4.0 s. What is the linear speed zcp o(2h ,boc6of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a;:e msjvoi7j + distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in em;v s:+ ji7oj12 minutes?

  A wheel of radius 1.0 m-eyvx: fx *0em is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on th0- yx*xfe :mvee wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in leng*bgf,+ u *;7gpsqkj gsth. If the motor rotates at the rate of 20 rev/s, what is the approximate linea; *7pkgs +fq*jubs ,ggr speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular se 83l2i71sqe wes qu x4e; -aq2+bckejpeed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheelc3q -jbqie;1ak+ se8 e272swux eq4 el's rim?

  What is the centripetaxw(* p ep *8gjl/*ahbta+al -wl acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike isj(a x pwtg*/laplb- +8 *hwe*a moving 8.00 m/s?

  How many revolutions pern1 xz8d,lff8 b minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an arbxf8 ,lfz1d8 ntificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radm,lchihotek: 9296k8jjdte oaao / 2(pban6 1ius 50 m with a speed of 20 m/s. The maximum centripeta en2ial9h6k, (had /toa9kjotboc6: m8e1j2pl force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a spe-opj /gnh2 7s/dn 8xqeed of 20 m/s. The maximum centripetal force (pr/pnhqdo 8n g-2 /sjx7eovided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, att v 1jvs* xoi+ma( qxcu.fc8)4tge1xa5ached to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that thex. j vxg *mc+ax8qu)oi5s(e1a1fvtc4 string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m dnr/u+utpk f )7own a lane at 4.3 m/7pk)/ftn + urus.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a constant angular acceleration of ptlf3h- 1.c+i.fn( *kg c7iood;qyr t $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a con8sdb , fylxn :m;rc12wstant angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m rad; y t-qfu8m0ytius automobile tire rotate after starting from rest and accelerating at a const ;t-tqu80y fymant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accel(,jis* sskr5 ,jvh4xz mhc c5(z,u9keqr*i6v eration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleratew.,kc9 /v,md-k(ow qtwln*su s with a constant angular accelera svwk,(q/d. 9u cwk,wom t-*nltion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches ae7 zoq u9c4is:h-fb 9xn angular speed of 6.0 rad/s while turning th:7i cef4 x 9qz-obsu9hrough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m+ t 4mns;)istwu ov/v-d g.a3g/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?+w s nd)4t /asug;-oim vv.3tg

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over -ujj,dy9x jih)::b y ja distance of hydb)i9j- jj:y: u jx,115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniforml5-9ii crbir8yo8q/aj y from 8.40 m/s to rest over a distance of 115 m. Hoi/c9r8j r8i ib5yaqo-w long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotat g3xks zqhr.1qkty00szbt3h* r11k. ves at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelervyqx0 k.k z*1tg1th1 q3hsr0bs.r kz3ation before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm loo2g,e5 kn04dwzqvda v/+l*9n e+bnr rng wrench is used, what is the magnitude of+4*ngnd rl5q 9rave 0v,kz/on dbw+ 2e the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a x(nbp ,d1lu e630 cm long wrench is used, what is the ed6,nxub(1 lpmagnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inmkzvj* ,vj)rq ,vw pq)(07 nhhertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled ask8z8b /d:lb)v1edf x2o9zci cgl l3j2 follows: mass m is at the origin, mass 2m is at x = a, and, mass 3e)xlb8 zdj/l31 l928ccodgki2: v bzfm is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictioy,s;(ele4exr tc ,o g s b/;kvm/10qatnless axis thought the center O. A rope wrapped4t ,axe0qb ks(ty ;;go/e ,vr1slm/ce around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought theoo( otk*ks /o*(gfz 6d center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another se(o k6 osk*ot(dfo* zg/ction of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. dd+t8 iwoa+us0qxe *: The rod is initially held in the horizontal position, and then released as the free end iq8 tusa+d *0id wo+:xes allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and +n 9;uktn6viti jp4k)mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm t9kk+)juti4;p 6 i nnvfor 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped ao3 2yconcadx :t3bhmzg+0 n 70round a frictionless disk pulley of mass 7.07 kg2c:n3x+ oa gd3 o t0zncb0yh7m and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fric q/3k7ie/k ryntionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratiok 3riy/q7ek/n n of the mass?

  A rotating flywheel can be used to store energy. If it is required a6g;)wm pw+ jhg.t(ns+hk rz4to store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of i546 2 j33kvwk -tz modtkhfwm4w-m z+rnertia of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and radius 0. 5t9 eo0 (;hqs pq9.nsppwkzw(010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of(w 5wt0 9p(p sk;q.hn9qs pzoe the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m nq0k;y4.e n 1x)9bnml e;nhwi rolls with a speed of 10 m/s. How high up an inclined plannel;k e.0b9ninxhmy1;wn) 4q e can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is relax5e7z,m4e1g+en lf z eased from rest and allowed to roll down e +1flmx7 ge,a nz4ze5an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rollsiokun;j3*m b a1u frt2c9u 2,j without slipping down a 35e incline that is 7jut uf jma ;2r un93,1*iokc2b.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum changes by2 2ka7 *i9vu5ddp pp/aaji1g j $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a momenkcvi0s zi6 d5+t of inertia of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s with arms extended has a moment of inee kjel5f+d7stojt, 9 5rtia ot ,7t95ofl5 jdkese +jf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?